and many more benefits!

Find us on Facebook

GMAT Club Timer Informer

Hi GMATClubber!

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

Hide Tags

T is the set of all numbers that can be written as the following sum [#permalink]

Show Tags

07 Jul 2008, 08:41

1

This post receivedKUDOS

13

This post wasBOOKMARKED

00:00

A

B

C

D

E

Difficulty:

95% (hard)

Question Stats:

33%(02:23) correct
67%(01:48) wrong based on 175 sessions

HideShow timer Statistics

T is the set of all numbers that can be written as the following sum involving distinct non-zero integers a, b, c and d: |a|/a + 2(|b|/b) + 3(|c|/c) + 4(|d|/d) + 5(|abcd|/abcd). What is the range of T?

Re: T is the set of all numbers that can be written as the following sum [#permalink]

Show Tags

07 Jul 2008, 09:10

My first thought is this:

|a|/a is going to be +/- 1...either positive or negative 1. The absolute value of any number divided by that number will be -1 or 1 because, for example if a = -4, then that is |-4|/-4, or 4/-4 = -1. But |4|/4 = +1.

The only thing I'm not sure about is the |abcd|/abcd. I think this should be the same...I came up with a range of 30.

On a number line, the farthest left it could be is -1 - 2 -3 -4 -5. And the most positive that it could be is 1 + 2 + 3 + 4 + 5. These equal -15 and +15 respectively. 15 - (-15) = 30.

nirimblf wrote:

T is the set of all numbers that can be written as a sum involving distinct real numbers a,b,c and d: |a|/a + 2(|b|/b) + 3(|c|/c) + 4(|d|/d) + 5(|abcd|/abcd). What is the range of T?

A. 15B. 20C. 28D. 29E. 30

It is an 800score question. Initially I guessed the solution. Then, reviewing it, it took me a few minutes and still I got it wrong. The solution isn't that complicated (try), but I really doubt if I could do it in 2 minutes. What do you think?

_________________

------------------------------------J Allen Morris**I'm pretty sure I'm right, but then again, I'm just a guy with his head up his a$$.

Re: T is the set of all numbers that can be written as the following sum [#permalink]

Show Tags

07 Jul 2008, 09:15

jallenmorris wrote:

My first thought is this:

|a|/a is going to be +/- 1...either positive or negative 1. The absolute value of any number divided by that number will be -1 or 1 because, for example if a = -4, then that is |-4|/-4, or 4/-4 = -1. But |4|/4 = +1.

The only thing I'm not sure about is the |abcd|/abcd. I think this should be the same...I came up with a range of 30.

On a number line, the farthest left it could be is -1 - 2 -3 -4 -5. And the most positive that it could be is 1 + 2 + 3 + 4 + 5. These equal -15 and +15 respectively. 15 - (-15) = 30.

That's what I initially thought. But note that abcd is positive if a,b,c,d are all negative, therefore |abcd|/abcd will be positive as well.

Re: T is the set of all numbers that can be written as the following sum [#permalink]

Show Tags

07 Jul 2008, 10:09

nirimblf wrote:

T is the set of all numbers that can be written as a sum involving distinct real numbers a,b,c and d: |a|/a + 2(|b|/b) + 3(|c|/c) + 4(|d|/d) + 5(|abcd|/abcd). What is the range of T?

A. 15B. 20C. 28D. 29E. 30

It is an 800score question. Initially I guessed the solution. Then, reviewing it, it took me a few minutes and still I got it wrong. The solution isn't that complicated (try), but I really doubt if I could do it in 2 minutes. What do you think?

Show Tags

Re: T is the set of all numbers that can be written as the following sum [#permalink]

Show Tags

08 Jul 2008, 08:56

Hi All

Answer is 29

|a|/a is going to be +/- 1...either positive or negative 1. The absolute value of any number divided by that number will be -1 or 1 because, for example if a = -4, then that is |-4|/-4, or 4/-4 = -1.

There is a gmat catch @ |abcd|/abcd, if all the numbers are negative, then minimum value will be -1-2-3-4 +5 (since multiplication of 4 -ves will become positive and 5 will remain positive)so min value = -5max value = 15Range = 20 in this case.

but if we take a = 1, b=-1, c = -1 and d = -1,then we will have min value = 1-2-3-4 -5 = -14and max value = 15

Re: T is the set of all numbers that can be written as the following sum [#permalink]

Show Tags

08 Jul 2008, 09:07

selvae wrote:

Hi All

Answer is 29

|a|/a is going to be +/- 1...either positive or negative 1. The absolute value of any number divided by that number will be -1 or 1 because, for example if a = -4, then that is |-4|/-4, or 4/-4 = -1.

There is a gmat catch @ |abcd|/abcd, if all the numbers are negative, then minimum value will be -1-2-3-4 +5 (since multiplication of 4 -ves will become positive and 5 will remain positive)so min value = -5max value = 15Range = 20 in this case.

but if we take a = 1, b=-1, c = -1 and d = -1,then we will have min value = 1-2-3-4 -5 = -14and max value = 15

so Range = 29

Hey I think min value should be -13 so Range comes out to be again 28
_________________

Re: T is the set of all numbers that can be written as the following sum [#permalink]

Show Tags

08 Jul 2008, 09:23

nirimblf wrote:

T is the set of all numbers that can be written as a sum involving distinct real numbers a,b,c and d: |a|/a + 2(|b|/b) + 3(|c|/c) + 4(|d|/d) + 5(|abcd|/abcd). What is the range of T?

A. 15B. 20C. 28D. 29E. 30

It is an 800score question. Initially I guessed the solution. Then, reviewing it, it took me a few minutes and still I got it wrong. The solution isn't that complicated (try), but I really doubt if I could do it in 2 minutes. What do you think?

I think the quickest way to answer this question has been posted by maratikus:

Re: T is the set of all numbers that can be written as the following sum [#permalink]

Show Tags

08 Jul 2008, 12:55

maratikus wrote:

nirimblf wrote:

T is the set of all numbers that can be written as a sum involving distinct real numbers a,b,c and d: |a|/a + 2(|b|/b) + 3(|c|/c) + 4(|d|/d) + 5(|abcd|/abcd). What is the range of T?

A. 15B. 20C. 28D. 29E. 30

It is an 800score question. Initially I guessed the solution. Then, reviewing it, it took me a few minutes and still I got it wrong. The solution isn't that complicated (try), but I really doubt if I could do it in 2 minutes. What do you think?

if it can be seen in one sought, it even doesnot take more than few seconds. i do not say its a 5 or 10 second question but definitely it should not be taking more than 30 sec. its basically a one sought question.
_________________

Show Tags

To build on that and just if you want to answer a more difficult question based on the same problem:

How many different elements does the set T contain ?

Nice question. Thirteen- curious if you have a quick way to get there. Clearly all the values in T are odd, which leaves at most 15 possible values (using the range), and 13 and 11 are clearly impossible. That leaves at most 13 elements in T, but verifying the rest of the possibilities are indeed in T seems to take a bit more work. I noted that if |abcd|/abcd = 1, then 15 and -5 are in T (for all positive and all negative signs), and if two of {a,b,c,d} are positive, |a|/a + 2(|b|/b) + 3(|c|/c) + 4(|d|/d) can take on any even value from -4 to 4, which means all positive odd integers from 1 to 9 are in T. Doing something similar for when |abcd|/abcd = -1 got me the rest of the odd negative values.
_________________

GMAT Tutor in Toronto

If you are looking for online GMAT math tutoring, or if you are interested in buying my advanced Quant books and problem sets, please contact me at ianstewartgmat at gmail.com

Re: T is the set of all numbers that can be written as the following sum [#permalink]

Show Tags

14 Apr 2015, 20:31

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________

Show Tags

T is the set of all numbers that can be written as the following sum involving distinct non-zero integers a, b, c and d: |a|/a + 2(|b|/b) + 3(|c|/c) + 4(|d|/d) + 5(|abcd|/abcd). What is the range of T?

A. 15B. 20C. 28D. 29E. 30

\(\frac{|x|}{x}\) is 1 when \(x>0\) and -1 when \(x<0\). For example, if \(x=2\), then \(\frac{|x|}{x}=1\) and if \(x=-2\), then \(\frac{|x|}{x}=-1\).

As for the minimum value: notice that all a, b, c, d and abcd cannot simultaneously be negative. For example if a, b, c and d are negative then abcd will be positive. Thus the minimum value is obtained when a is positive and b, c and d are negative: 1-2-3-4-5=-13.